Why is my light shining though my object when the smoke is on?
Smoke is made up small particles, gases and water vapor. Water vapor
  makes up the majority of smoke.


When light passes through smoke, it reflects off these particles into the camera. That's why you can shine a light/laser beam through mist/smoke in real life and get the same effect. 

See https://www.youtube.com/watch?v=fU6JNGxfxnY

Edit:

According to the Blender manual here:


  Clip Start:
  Distance from the light object at which the shadow map starts. Any object before this distance will not appear to cast shadows. Clip Start will only appear for point, spot and area lights.
  
  Contact Shadows This type of shadow exists to fix light leaking caused
  by bias or shadow map undersampling. It uses the depth buffer to find
  occluders (just like Screen Space Reflections). However, just like
  Screen Space Reflections it has the same limitations, namely, unknown
  object thickness and effect disappearing at screen edges.


Unfortunately, no matter how much I played with the light settings, I couldn't get rid of the lighting issues. I thought that maybe it was the holes in the mesh that was causing the issue, but replacing the light housings with inset cylinders didn't work either.

I found a solution, but its just a makeshift coverup for the issue. The result is shown below:



And here's the secret behind the scenes madness: